Recent times have seen an increase in the use of data converters, especially those used in audio signal processing. Signal processing is typically done by digital filters, such as, Finite Impulse Response (FIR) filters and Infinite Impulse Response (IIR) filters. The main objective of signal processing is to convert an analog signal to a digital signal and then to convert the digital signal back to the analog signal. An analog signal is converted to a digital signal because sometimes the signal cannot be readily transmitted in the analog form. Therefore, to ensure effective transmission of the analog signal from place to another, the analog signal is first converted to a digital form and then transmitted. Thereafter, the digital signal is converted back to the analog form.
The two basic signal processing functions are decimation and interpolation. Broadly, decimation can be termed as a process of down converting the sampling frequency of a signal so that a lesser amount of memory is used to transmit the signal in digital form. Also, decimating a signal to an appropriate frequency, like the Nyquist frequency, ensures that when the signal is converted back to analog form, the resultant analog signal does not deviate greatly from the original analog signal. Interpolation, on the other hand, is the process of “filing the gaps” in the generated analog signal to get a signal similar to the original analog signal.
A typical decimator or a digital down converter for handling a large rate change uses a high order decimator filter chain. Such a conventional high order decimator filter chain may comprise a large number of multipliers and long filters. An efficient approach for reducing the number of multipliers in implementing such a high order decimator chain can be achieved by replacing the high order decimation chain with a cascaded integrator comb (CIC) filter.
CIC filters are based on adders and subtractors, as opposed to multipliers in conventional decimators. CIC filters are built using integrator and comb filter pairs and are capable of multi-rate processing. CIC filters are specifically used in a variety of applications such as hardware quadrature modulation and demodulation in modern wireless systems and delta-sigma analog-to-digital and digital-to-analog converters. In effect, CIC filters act as narrowband low pass filters and are economical in comparison to conventional FIR filters.
In spite of the increased use of CIC filters, they may have certain limitations. One of the limitations is the soft frequency roll off, as compared to the sharp frequency roll off in the case of a low pass FIR filter. Such a soft frequency roll off results in a wide transition region and a non-flat pass band. Also, for a more faithful and acceptable imaging or alias rejection, the order of the CIC filter has to be increased. Increasing the order of the CIC filter results in increased droop in the pass band. Typically, this droop in the pass band can be countered by using a compensating non-recursive FIR filter cascaded with the CIC filter. However, the compensating non-recursive FIR filter works at a low sampling rate and introduces a constant group delay in the output signal of the complete filter sequence. Further, the tap length of the compensating non-recursive FIR filter is dependent upon the stop band attenuation used before decimation and the order of the CIC filter.
The tap length of the compensating non-recursive FIR filter is dependent on the order of the CIC filter and the pass band bandwidth. In the case where the order of the CIC filter or the pass band bandwidth is increased, the tap length of the compensating non-recursive FIR filter may also be increased to achieve appropriate compensation against the droop in the pass band caused by the CIC filter. For example, a fourth order CIC filter would use a 60-70 tap FIR filter for achieving a decent in band signal-to-noise ratio (SNR).
A large tap length FIR filter is difficult to implement and causes a high area penalty on the ever-decreasing silicon area available to designers. Further, the large tap length FIR filter operates at a frequency greater than the Nyquist rate, thereby increasing the overall power consumption. Also, the increasing number of coefficients in the large tap length filter may increase the filter complexity. This effectively increases the number of memory elements and multipliers, the original problem that the CIC filter solved by replacing the high order decimation or interpolation chain.
In light of the above, there is a need for a method and system for addressing the use of the large tap FIR filters to compensate for the droop in the frequency response of a signal. The system should not use large memory elements and should not increase the overall power consumption. Also, the method and system should not use a large area of the available silicon area.